7) CHAPTER 1. VECTOR ANALYSIS AND MAXWELL'S EQUATIONS IN INTEGRAL FORM

azDE=2a,, ct<r <b

F. f (. I

$(t,n) 'ds=

l,Pdv = J,.r,"ot,* J,,-P,dto=o

For r>b,

Forr<a

Forr>a

.'. E=0

a'D(b) E=--Ta-,er'

a<r <b

:. E oE = 4 ^, = z * rcu 4cos(to'r)a.

t, = fi@,n) = -2 xtoo { sin(t o' r)a,

1.37

4npo rs

Ja-

8ttp, -,15

23

r.38

... E- E,n,=+4, r>ar r l5t.ttfQe"E'ds= | pdvJs " Jv

I =L= to-,t, =lx loo =3183 1fum2)A z.l0- E

,r 3 183:. p, = ;= #= 3.183x l0{ (C/mr)

For p < a, the Gaussian surface is a cylinder with radius p and height I-

.'. $t,E 'ds= p,'lTP!LJs

pL p2t

I I e,,E"pdQdz- p,ttd LJo Jo

^ -^2tE-=P-'oP

t =1.59x rc^L=l.l6xloj po 2re.p €o

E= Erar=1.'76xlo1 pto (v/m) , P < a

For p>a

$,t," ds- p".trnzL

p.,7w'Le 2ntop

t|76xlo'4ap

t.te xrcl4-p

p>4

(a) emf ={"n a7 =-fi\y a'

fn a, = l. l."u['-(#l]"natp'd@p

= zrn ",,n

att [ol, - (#)')+t r'

- * 1," ds = -2*a+,(t - #)",, *

=zonft- Po lrrn,"L 2 0.091

24 CHAPTER 1. VECTOR ANALYSIS AND MAXWELL'S EQUATIONS IN INTEGRAL FORM

{s al =znpEo

r f ( i - l-\"orrr-l =-s-s6o,B"p(o'os- 2pz)coscutr=hl-2"'n'17 o.oe/ I

E = ErNo= -5.56ial8,p(O'Oe - 2pz)cosaa,

1.40 emf = - *l: o" = - *! r.2sin 103 rds = - ftlo'tx 0'2 sin 103 t) = -20cos 103 r

, = $ = J(-zo"otio3t) = -4cos1o3t (A)

l.4l ds= dxdY^,

emr = -*J,t ^=-*J,Vcos103r(a, *^,)'d*dv''

= -fr(o.us"H.o"o")= "'rt"n to3t (v/m)

(b)

o['-(#)'l

5.56a8"p(o.09 -20')

26 CHAPTER I. VECTOR ANALYSIS AND MAXWELL'S EQUATIONS IN INTEGRAL FORM

r.44 6I .av = | t.a"J"Fo Js

(a)p<a

Jr.a, = o

.'. B=0

= I" I)rr'r'op'do = f'[30""",*]"-

(b) a< p<b

Ir o'

= I" Ib' - u')ao = 3(o' - "'),t"*['

4tt, , i\= ;(P- -a /

6L al =2oP BJ, F,, rt,, a

.'.B,=+ry2u (ot -a')B=B.a. - ! '.a,qq 3 p

(c) p> bp pznpb Ltr, ^

J,J. * = J. J"

2p'p'dpdQ= f(b' - u')

... B _ lr" .91u,_a,)=?!n(u,_u,)e 2np 3' ' 3 p \ /

B=Brar=?u"(0,-",)i",

1.45 (a) 6L oZ = | J'a"= rJ, Fo Js

e2" B.| 'pdQ=lJo p"

2'7

UI UIB.=z-'""COSA|' 2np 2rP

UIB = B

^a ^ - ---e--e- cos AtA,ee 2np

(b) i.

w^= l"n a'

ii' "* = -oY: = -*l#"o"atnff)= ry'"4J!"in'o_ ltol cosatt

2ttp

emr = -*|" ^=-*f]Ji",A#r*= -*lo "';t;'"* '"ffi]=

o o384,'lsincrr

= f, f '

#cosadpdz = t-Jl-"**^+

t.46 Ba